The density function of $X$ is given by $$f(x) = \begin{cases} a + b x^2 & \mbox{ if } 0\le x\le 1\\ 0 & \mbox{ otherwise }\end{cases}.$$ If the expectation of $X$ is $E(X)=0.6875$, find $a$ and $b$.
$a=$
$b=$